Technically speaking, nearly half the of the US fighters in WWII were descendants of previous designs.
The P-38, P-39, P-51 and F4U are exceptions to this.
The P-40 has just been discussed at length.
The F6F came from the F4F, which came from the F3F, which came from the F2F.
The P-47 came from the P-43, which came from the P-35, which came from the SEV-3 (SEV-1XP/SEV-7).
Another good example, while not a fighter, would be the C-47, which was developed from the DC-3, which was developed from the DC-2, which was developed from the DC-1.
This is basically my point - another classic example which I previously mentioned being Blenheim, Beaufort and Beaufighter. Blenheim and Beaufighter shared many of the same jigs and so on, but they were really quite different - night and day in terms of capabilities and versatility. Same with LaGG-3 / La 5 family.
However it is also true that sometimes within the same designation a given aircraft can change enormously. I really don't think the Fw 190D is the same aircraft as the 190A, nor the Spit XXI to the Spit I. It is somewhat subjective, which always seems to get us in trouble around here.
My point about the P-36 vs. P-40, is that the older design, the P-36, had already reached it's peak of performance before the war. It basically hit a wall both in terms of speed and carrying capacity. The difference did indeed boil down mainly to the engine but that change happened to dramatically change the aircraft.
It had a wright 1670 engine 900 hp, an early Wright 1820 Cyclone (950 hp), Pratt and Whitney 1830 Twin Wasp (900 hp, 1100 or 1200 hp depending on the subvariant), and the later model Wright Cyclone R-1820 G 205 (1200 hp) but it never made it past about 320 mph. It had a relatively slow dive acceleration though good high speed handling which showed hope for the design family so to speak. They experimented with some modern combat features like armor and heavier guns but it was limited in the weight capacity it could carry. Most were underarmed with 4 or 6 .30 caliber guns.
The P-40 started at 1000 hp (and was already 40 mph faster than the P-36) and went up to 1350 or 1500 hp (in official max boost rating) and speed went from 340 mph to 370 mph in mid 1942. By the end of 1941 variants with 6 heavy machine guns were standard.
The P-36 had 5 victory claims for the US, 269 for France (mainly in the Battle of France - with 7 aces- and another five or ten in Vichy use mainly at Morocco) and about two dozen with the RAF mainly in the CBI.
Total victory claims definitely less than 300.
By contrast
P-40 pilots made 2,225 victory claims for the US alone, making it the 5th ranked fighter in US use (ahead of the Wildcat and Corsair) with at least 80 USAAF Aces flying the type, it had about 130 claims for the RAAF and 100 for RNZAF just in the Pacific, and a large but unknown (to me) number by the RAF / Commonwealth in the Med where it was in heavy use for four years and was the main air superiority fighter for the most crucial period (at least several hundred claims and they had 46 Aces flying P-40s) or USSR (again, at least several hundred claims and they too had about 40 Aces flying the P-40 and multiple VVS units made 'guards' status while equipped with that aircraft). As a fighter bomber of course it also famously helped fill the CAS gap where existing Allied light, dive and medium bombers failed.
The Hawk hit a wall in terms of it's speed and carrying capacity in the 1930s. It couldn't have done what the Tomahawk and Kittyhawk did. Like the Hurricane the P-36 could survive in 1940 but would suffer in 1941 or 1942 in the same kind of areas, let alone 1943. You wouldn't be flying fighter sweeps or escort missions over enemy airfields in P-36s in 1943 I'll put it that way. They were certainly of the same DNA and very closely related, but I stand by my claim that the P-40 was a different aircraft. If we really have to I can start enumerating the specific features and design elements (Shortound already pointed out some of the changes to the wing) but ultimately it's a subjective opinion so I know some people will never change their minds on it. I doubt I will either as I've done enough research on the type to be pretty confident of my opinion on this. But I'm willing to be surprised by new evidence I hadn't considered.